HOURS STUDYING AVG GRADE

0 62
1 78
2 85
5 74

WHICH TYPE OF FUNCTION IS MOST LIKELY TO MODEL THESE DATA?

A. LINEAR FUNCTION W/POSITIVE SLOPE
B. LINEAR FUNCTION W/NEGATIVE SLOPE
C. NON-LINEAR THAT DECREASE THE INCREASE
D. NON LINEAR FUNCTION THAT INCREASES THEN DECREASES

HOURS STUDYING----- AVG GRADE

0-------------------- 62
1-------------------- 78
2-------------------- 85
5-------------------- 74

WHICH TYPE OF FUNCTION IS MOST LIKELY TO MODEL THESE DATA?

A. LINEAR FUNCTION W/POSITIVE SLOPE
B. LINEAR FUNCTION W/NEGATIVE SLOPE
C. NON-LINEAR THAT DECREASE THE INCREASE
D. NON LINEAR FUNCTION THAT INCREASES THEN DECREASES

To determine which type of function is most likely to model the given data, we need to analyze the relationship between the hours studying and the average grade.

Looking at the data, we observe that as the hours studying increase, the average grade generally increases until a certain point where it starts to decrease. This means that initially, the relationship is positive (as the hours studying increase, the average grade also increases), but after a certain threshold, the relationship becomes negative (as the hours studying increase further, the average grade decreases).

Based on this understanding, we can conclude that the data suggest a non-linear function that initially increases and then decreases.

Therefore, the most likely type of function to model these data is D. NON-LINEAR FUNCTION THAT INCREASES THEN DECREASES.